The First Law of Thermodynamics Chapter 19 The First Law of Thermodynamics

Goals for Chapter 19 To represent heat transfer and work done in a thermodynamic process and to calculate work To relate heat transfer, work done, and internal energy change using the first law of thermodynamics To distinguish between adiabatic, isochoric, isobaric, and isothermal processes To understand and use the molar heat capacities at constant volume and constant pressure To analyze adiabatic processes

Introduction A steam locomotive operates using the laws of thermodynamics, but so do air conditioners and car engines. We shall revisit the conservation of energy in the form of the first law of thermodynamics.

Thermodynamics systems A thermodynamic system is any collection of objects that may exchange energy with its surroundings. In a thermodynamic process, changes occur in the state of the system. Careful of signs! Q is positive when heat flows into a system. W is the work done by the system, so it is positive for expansion. (See Figure 19.3 at the right.)

Work done during volume changes Figures 19.4 and 19.5 below show how gas molecules do work when the gas volume changes.

Work on a pV-diagram The work done equals the area under the curve on a pV-diagram. (See Figure 19.6 below.) Work is positive for expansion and negative for compression. Follow Example 19.1 for an isothermal (constant-temperature) expansion.

Work depends on the path chosen Figure 19.7 below shows why the work done depends on the path chosen.

First law of thermodynamics First law of thermodynamics: The change in the internal energy U of a system is equal to the heat added minus the work done by the system: U = Q – W. (See Figure 19.9 at the right.) The first law of thermodynamics is just a generalization of the conservation of energy. Both Q and W depend on the path chosen between states, but U is independent of the path. If the changes are infinitesimal, we write the first law as dU = dQ – dW.

Cyclic processes and isolated systems In a cyclic process, the system returns to its initial state. Figure 19.11 below illustrates your body’s cyclic process for one day. A isolated system does no work and has no heat flow in or out.

Working off dessert Study Problem-Solving Strategy 19.1. Follow Example 19.2 to see if exercise is an easy way to make up for a caloric splurge. Follow Example 19.3 using Figure 19.12 at the right.

Comparing two processes and a phase change Follow Example 19.4 to compare two thermodynamic processes. Use Figure 19.13 at right. Follow Example 19.5 on boiling water.

Four kinds of thermodynamic processes Adiabatic: No heat is transferred into or out of the system, so Q = 0. Isochoric: The volume remains constant, so W = 0. Isobaric: The pressure remains constant, so W = p(V2 – V1). Isothermal: The temperature remains constant.

The four processes on a pV-diagram Figure 19.16 shows a pV-diagram of the four different processes.

Internal energy of an ideal gas The internal energy of an ideal gas depends only on its temperature, not on its pressure or volume. The temperature of an ideal gas does not change during a free expansion. (See Figure 19.17 at the right.)

Heat capacities of an ideal gas CV is the molar heat capacity at constant volume. Cp is the molar heat capacity at constant pressure. Figure 19.18 at the right shows how we could measure the two molar heat capacities.

Relating Cp an CV for an ideal gas Figure 19.19 at the right shows that to produce the same temperature change, more heat is required at constant pressure than at constant volume since U is the same in both cases. This means that Cp > CV. Cp = CV + R.

The ratio of heat capacities The ratio of heat capacities is  = Cp/CV. For ideal gases,  = 1.67 (monatomic) and  = 1.40 (diatomic). Table 19.1 shows that theory and experiment are in good agreement for monatomic and diatomic gases. Follow Example 19.6.

Adiabatic processes for an ideal gas In an adiabatic process, no heat is transferred in or out of the gas, so Q = 0. Figure 19.20 at the right shows a pV-diagram for an adiabatic expansion. Note that an adiabatic curve at any point is always steeper than an isotherm at that point. Follow the derivations showing how to calculate the work done during an adiabatic process.

Adiabatic compression in a diesel engine Follow Example 19.7 dealing with a diesel engine. Use Figure 19.21 below.